Abstract:

Local existence, global existence and nonexistence of c
lassical solutions for a degenerate and strongly coupled quasilinear parabolic s
ystem were studied. Regularization method and a prior estimate skills were used
to obtain the local existence of classical solutions. Moreover, sufficient condi
tions were given for the existence and nonexistence of global classical solution
s. The results show that the problem admits a global solution when the intrasp
ecific competitions are strong; whereas there exists no global solution when the
species are strongly mutualistic.

Key words: degenerate parabolic system, strongly coupled, global existence, global nonexistence